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Figs. 9-11 show the design exploration of various funicular funnel shells generated with the tool. The variations of equilibrium networks in Fig. 9 are realized by simply changing the definition of free or fixed support nodes, the latter marked with blue dots. The only other modification of the diagrams is the uniform scaling of the edges of the force diagrams. The force diagrams are drawn to the same scale so that the overall magnitude of the horizontal thrusts in each structure can be visually compared. Based on these simple modifications during the design exploration process, the resulting funicular funnel shells (Figs. 9a-f) vary greatly in shape and spatial articulation.

Fig. 9 Design exploration of various funicular funnel shells (a-f) (the tension elements are highlighted in blue) by changing the definition of free or fixed support nodes (marked with blue dots) and the overall magnitude of the horizontal thrusts in each structure

The integration of holes in the shell surface as shown in Fig. 10 demands the topological modification of the form diagram. These openings always form a funicular polygon in the form diagram and are by definition convex; their force equilibrium in the force diagram has a star-shaped topology (Rippmann & Block 2013). The cantilevering ridge edge can be seen as an inverted opening forming a convex boundary.

Fig. 10 Design exploration of various funicular funnel shells with openings

Further, the TNA framework allows controlling the multiple degrees of freedom in statically indeterminate networks. In other words, a statically indeterminate form or force diagram can be geometrically modified while keeping horizontal equilibrium. This means that the length of corresponding elements of the form and force diagram can be modified while guaranteeing their parallel configuration and direction. Consequently, this leads to a local or global increase or decrease of forces since the length of each element in the force diagram represents the horizontal force component of the corresponding element in the structure. In Fig. 11, the force diagram in (b) shows the local attraction of horizontal thrust towards the centre of the structure resulting in a local compression ring and hence a crease in thrust network. It is important to note though that, in contrast to compression shells with fixed supports, the freedom to change the force distribution of structures with continues tension ties is limited due to the geometrically much more strongly constrained force diagram.

Fig. 11 A different force distribution for the same form diagram Γ in (a) and results in a crease in the equilibrium network G of (b)